A336207 Lexicographically earliest sequence of nonnegative terms such that whenever a(k_1) = ... = a(k_m) with k_1 < ... < k_m, the sum k_1 + ... + k_m can be computed without carries in factorial base.

0, 0, 1, 2, 3, 0, 2, 0, 4, 5, 6, 1, 5, 4, 7, 8, 9, 3, 10, 11, 12, 13, 14, 0, 8, 1, 11, 10, 15, 0, 16, 7, 17, 16, 18, 2, 19, 17, 20, 21, 22, 15, 23, 24, 25, 26, 27, 0, 13, 12, 24, 19, 28, 1, 21, 20, 29, 30, 31, 6, 30, 29, 32, 33, 34, 28, 35, 36, 37, 38, 39, 2

Offset: 1

Author

Rémy Sigrist, Jul 12 2020

Keywords

• nonn
• look
• base

Examples

			In factorial base:
- 1 = "1", 2 = "10", 3 = "11", 4 = "20",
- we can add without carry 1 and 2, so a(1) = a(2) = 0,
- 1 + 2 + 3 implies a carry, so a(3) = 1,
- 1 + 2 + 4 and 3 + 4 imply a carry, so a(4) = 2.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to factorial base representation
• Rémy Sigrist, C program for A336207

Crossrefs

See A279125 and A336206 for similar sequences.

Cf. A279732.

Programs

C

See Links section.

Formula

a(n) = 0 iff n belongs to A279732.